Question

A psychologist needs 12 left-handed subjects for an experiment, and she interviews 15 potential subjects. About 10% of the population is left-handed. What is the probability that exactly 12 of the potential subjects are left-handed?

Answer 1

The probability that exactly 12 of the potential subjects are left-handed is approximately 0.0015.

Step-by-step explanation:

To find the probability that exactly 12 of the potential subjects are left-handed, we can use the binomial probability formula:

P(x) = C(n, x) * p^x * (1 - p)^(n - x)

Where:

• P(x) is the probability of getting exactly x successes
• C(n, x) is the number of combinations of n items taken x at a time
• p is the probability of success (10% or 0.1 in this case)
• n is the total number of trials (15 in this case)
• x is the number of successful trials (12 in this case)

Plugging in the values:

P(12) = C(15, 12) * (0.1)^12 * (1 - 0.1)^(15 - 12)

Calculating the values:

P(12) = 455 * 0.1^12 * 0.9^3

Finally, we can calculate the probability:

P(12) ≈ 0.001475411